曲线中的切线问题

导数是解决函数的单调性、最值、不等式证明等问题的有力工具,其应用相当广泛,因而是每年高考考查的重点与热点,但考生在这里失分较多,利用导数求曲线的切线方程是导数的重要应用之一,本文对此问题进行探索研究,归纳总结出了几种常见问题,供广大教师和同学们参考．     

曲线中的切线问题

导数是解决函数的单调性、最值、不等式证明等问题的有力工具,其应用相当广泛,因而是每年高考考查的重点与热点,但考生在这里失分较多,利用导数求曲线的切线方程是导数的重要应用之一,本文对此问题进行探索研究,归纳总结出了几种常见问题,供广大教师和同学们参考.1.给定切点的曲线切线问题例1求曲线y=xex+2x+1在点(0,1)处的切线方程.解因为点(0,1)在曲线y=xex+2x+1     

有限离散函数的导数和性质

通过引入有限离散函数的导数概念,分别从几何直观和性质两个角度,比较了有限离散函数的导数概念和常规连续函数导数的相似性.结果表明,在局部情况下,有限离散函数导数近似等于连续情形下的导数.在运算性质上,有限离散函数导数的性质非常相似于连续情形时的导数性质.最后的例子给出了有限离散函数导数的一个应用.     

关于导数的复习

导数在高考中具有工具性的作用 ,主要表现在两个方面 :1)应用导数探索函数的单调、极值等性质及其在实际中的应用 ;2 )应用导数确定曲线的切线斜率 .这样一来 ,原来用初等方法难以解决的问题显得轻松 ,从而使函数、曲线这两大考查重点的命题范围得以拓展 .比如 ,在解析几何中 ,我们一般只求圆的切线 ,有了导数 ,我们会很方便地求曲线 y =x3-a ,y =1-axx 在点M (x1,f(x1) )处的切线 (参见2 0 0 2年高考题 ) ;仅从不等式的内部考虑 ,我们很难证明当x >1时 ,不等式x >ln(1+x)成立 ,有了导数 ,我们就可以利用函数 f(x) =x -ln(1+x)的单调性来证…     

圆锥曲线中一类斜率为定值问题的高等背景与初等解法

本文从一道椭圆试题出发,探索圆锥曲线中一类斜率为定值问题的解法,先利用高等数学中的极限思想与导数方法探求这个定值,然后再利用初等解法给出证明.     

集值优化问题的Benson真有效解的广义导数型最优性条件

引进了集值映射关于锥的Clarke切导数, Adjacent切导数与Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型最优性条件．     

广义扰动映射的上导数

主要讨论了两集值映射和的上导数．在比标准约束品性弱的条件下得到了两个集值映射和的上导数与两集值映射上导数的和之间的包含关系,并将此结论用于讨论广义扰动映射的上导数,得到广义扰动映射的上导数的上界估计．     

聚焦导数定义

导数是高中数学的新增内容,为高中数学 注入了新的活力,利用导数可从更深的角度来 研究函数的性质.本文聚焦导数定义,对平时 遇到的有关导数概念的题目分类分析,以期加 深对导数概念的理解和应用. f(x)在点x0处的导数:     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

紧扣“细节”,让高中数学导数难题不再难

随着新课改的不断发展与深化,高中数学课本教材中关于导数内容在编排结构和内容安排上发生了较大的变化,淡化极限突出导数是最明显的变化;导数已经发展成为高中数学课程教学的重要内容,同时也是处理函数难题必不可少的重要"利器";近年来,导数是高考中必考内容之一;实践表明:高考中导数考查主要涉及导数的概念与意义、运算法则与公式、综合应用等;不少学生对于导数难题存在一定的惧怕心理,在处理实际问题的过程中,稍有不慎就容易掉入导数难题所设置的     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.